# Book:Frank Ayres, Jr./Theory and Problems of Differential and Integral Calculus/SI Edition

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## Frank Ayres, Jr. and J.C. Ault:

## Frank Ayres, Jr. and J.C. Ault: *Theory and Problems of Differential and Integral Calculus (SI Edition)*

Published $\text {1972}$, **Schaum**

- ISBN 07 084395 3.

### Subject Matter

### Contents

- Preface to Second Edition (March 1964)

**Chapter 1**: Variables and Functions**Chapter 2**: Limits**Chapter 3**: Continuity**Chapter 4**: The Derivative**Chapter 5**: Differentiation of Algebraic Functions**Chapter 6**: Implicit Differentiation**Chapter 7**: Tangents and Normals**Chapter 8**: Maximum and Minimum Values**Chapter 9**: Applied Problems in Maxima and Minima**Chapter 10**: Rectilinear and Circular Motion**Chapter 11**: Related Rates**Chapter 12**: Differentiation of Trigonometric Functions**Chapter 13**: Differentiation of Inverse Trigonometric Functions**Chapter 14**: Differentiation of Exponential and Logarithmic Functions**Chapter 15**: Differentiation of Hyperbolic Functions**Chapter 16**: Parametric Representation of Curves**Chapter 17**: Curvature**Chapter 18**: Plane Vectors**Chapter 19**: Curvilinear Motion**Chapter 20**: Polar Coordinates**Chapter 21**: The Law of the Mean**Chapter 22**: Indeterminate Forms**Chapter 23**: Differentials**Chapter 24**: Curve Tracing**Chapter 25**: Fundamental Integration Formulas**Chapter 26**: Integration by Parts**Chapter 27**: Trigonometric Integrals**Chapter 28**: Trigonometric Substitutions**Chapter 29**: Integration by Parts**Chapter 30**: Miscellaneous Substitutions**Chapter 31**: Integration of Hyperbolic Functions**Chapter 32**: Applications of Indefinite Integrals**Chapter 33**: The Definite Integral**Chapter 34**: Plane Areas by Integration**Chapter 35**: Volumes of Solids of Revolution**Chapter 36**: Volumes of Solids with Known Cross Sections**Chapter 37**: Centroids**Chapter 38**: Moments of Inertia**Chapter 39**: Fluid Pressure**Chapter 40**: Work**Chapter 41**: Length of Arc**Chapter 42**: Area of Surface of Revolution**Chapter 43**: Centroid and Moment of Inertia**Chapter 44**: Plane Area and Centroid of Area**Chapter 45**: Length and Centroid of Arc. Area of Surface of Revolution**Chapter 46**: Improper Integrals**Chapter 47**: Infinite Sequences and Series**Chapter 48**: Tests for Convergence and Divergence of Positive Series**Chapter 49**: Series with Negative Terms**Chapter 50**: Computation with Series**Chapter 51**: Power Series**Chapter 52**: Series Expansion of Functions**Chapter 53**: Maclaurin's and Taylor's Formulas with Remainders**Chapter 54**: Computations using Power Series**Chapter 55**: Approximate Integration**Chapter 56**: Partial Derivatives**Chapter 57**: Total Differentials and Total Derivatives**Chapter 58**: Implicit Functions**Chapter 59**: Space Curves and Surfaces**Chapter 60**: Directional Derivatives. Maximum and Minimum Values**Chapter 61**: Space Vectors**Chapter 62**: Vector Differentiation and Integration**Chapter 63**: Double and Iterated Integrals**Chapter 64**: Centroids and Moments of Inertia of Plane Areas**Chapter 65**: Volume under a Surface. Double Integration**Chapter 66**: Area of a Curved Surface. Double Integration**Chapter 67**: Triple Integrals**Chapter 68**: Masses of Variable Density**Chapter 69**: Differential Equations**Chapter 70**: Differential Equations of Order Two**INDEX**

## Further Editions

## Source work progress

- 1972: Frank Ayres, Jr. and J.C. Ault:
*Theory and Problems of Differential and Integral Calculus*(SI ed.) ... (previous) ... (next): Chapter $1$: Variables and Functions

Integrals:

- 1972: Frank Ayres, Jr. and J.C. Ault:
*Theory and Problems of Differential and Integral Calculus*(SI ed.) ... (previous) ... (next): Chapter $25$: Fundamental Integration Formulas: $27$.